Monday, December 9, 2013

What is Rarity?

Editor's Note - While the text of the post below remains relevant, in November 2015 the FWGNA database was expanded to include 6.5% additional records and 2 new species. See the current FWGNA Synthesis page for our most recent analysis.

In recent weeks I have received some very generous compliments
regarding the brand new “Synthesis” of freshwater gastropod abundance posted on
the FWGNA site. Essentially what my
colleagues and I have done is delete the old “Recommendations” pages that used
to be available separately from the FWGGA, FWGSC, FWGNC and FWGVA sites and
replaced that little corner of cyberspace with a combined analysis of the “distribution
of commonness and rarity” across all 67 species of freshwater gastropods (11,471 records) inhabiting the Atlantic drainages of the United States, from Georgia to the New
York line [1].

My initial motivation was simply to expand (and formalize)
the analysis I first proposed on this blog in January 2012 [2], adding data
from five Mid-Atlantic states to data already in hand for the four states
further south. I confess that I was a
bit disappointed, however, when the enlarged dataset did not fit a lognormal
model this second time around, because I had already written a nice discussion
section explaining why it should, and exploring all manner of elaborate
implications about broad-scale ecological relationships in this diverse
assemblage of freshwater gastropods over evolutionary time. But I was teetering on the ragged edge of
rejecting the lognormal in January 2012, with my Shapiro-Wilk W barely
nonsignficant at p < 0.065, and an additional 2,597 records (and 10 species)
pushed me off to p < 0.032. So the
new FWGNA “Synthesis” is entirely nonparametric. Such is science.

During the literature review for this most recent analysis I
came across a little jewel of a book which I think deserves a wider audience:
“Rarity” by a (then) Fellow at the British Museum, Kevin J. Gaston [3]. The
first chapter of Gaston’s book offers an especially insightful dissection of
the meaning of the adjective, “rare,” beginning with all the dictionary
definitions and proceeding through (what seems to be, almost!) every imaginable
scientific usage in modern history.

The author takes as a given that the adjective “rare” must be
a comparative term. Things can only be
rare relative to other things, which are called common. At
first blush, it might seem odd that Gaston does not explicitly consider such
“absolute rarity” measures as seem to be popular in state natural heritage agencies
here in the USA. For example, North
Carolina botanists define “significantly rare” as “generally with 1 – 100
populations in the state,” apparently unscaled by anything [4]. But the (unstated) implications of such an
approach must be that plants with greater than 100 populations are
insignificantly rare in North Carolina, and that the significants are rare
relative to the insignficants. If my
wife passes me a trapezoidally-shaped bowl with 100 red candies in it, I would
not consider red candy to be rare. But
if the bowl contained 100 red candies and 1000 browns, I might.

Now if there are more than two colors of candy in the bowl, say
100 red, 500 green, and 1000 brown, an additional complication may arise. Perhaps the rareness of red remains unchanged,
as 100/1000 or 100/1100? Or perhaps red
is now even more rare, as 100/1600? Or
perhaps rareness is best expressed as 1/3, unweighted by frequency? The most interesting analysis in Gaston’s
Chapter 1 is his demonstration that the most robust definition of a rare
species is “the x% with the lowest
abundances or smallest range sizes in the assemblage.” Gaston would prefer the rank statistic for
his bowl of candy, the rareness of red being 1/3.

Back in my essay of January 2012, I expressed a concern that
most of the literature (with which I was familiar at the time) focused on the
rarity of individuals within communities.
So if F. C. Baker’s samples of Oneida Lake contained 32 species, with
Planorbula armigera ("jenksii") the least abundant (just N=1 individual), everybody will concur that Planorbula is rare in Oneida Lake [5]. But FWGNA data are incidences across a wide
geographic area, not individuals within a single community. So if the fauna of US Atlantic drainages from
Georgia through Pennsylvania comprises 67 species, and Aplexa hypnorum is found
in the lowest number of sample sites (just N=1 pond), is Aplexa rare in the
same sense that Planorbula is rare?

Yes, Gaston reassures us that any technique we might apply
to analyze the abundance-rarity of snail individuals within a single lake will generalize
to the incidence-rarity of snail populations across nine states. Note that his definition of rarity above
makes no distinction between “lowest abundances or smallest range sizes.” The ecological causes for these two types of
rarity most certainly do differ, but the analytical consequences are the same.

Ultimately, although some statistics to measure rarity are
more robust than others, the dividing line between rare and common must need be
a subjective decision. So what is a
reasonable value for “x” in Gaston’s definition three paragraphs above? Gaston’s remarkably insightful first chapter
also includes a Table 1.4 reviewing 20 studies (mostly of plants and birds) in
which the authors have both defined the word “rare” and provided data sufficient
to calculate rarity, in its “proportion of species” sense [6]. And Gaston’s judgment suggested to him that a
fair consensus might be 25%.

So ultimately, Gaston settled on what he called “the quartile definition,” defining rare
species as the 25% with the lowest abundance or lowest incidence. And this is the definition we have adopted
for the FWGNA project as well, expanding Gaston’s concepts across the entire nine-state
study area to elaborate a five-tiered system.
We elect to set aside the rarest 5% of the freshwater gastropod species
in a special incidence category I-5, leaving the next 20% as I-4, and
successive (increasingly widespread) quartiles I-3, I-2, and I-1.

So now that we have defined rarity, what are its
causes? That might be suitable grist for
a future post. But in closing I probably ought to re-emphasize the main point of the present essay, which at one time I should
have imagined might be obvious to all my colleagues in this field, but which (I
now have some reason to fear) may be lost on some.

Among the more colorful comments I received regarding my
post of 9Sept13 [7] was the following:

“You also go on about how this or that COMMON species of
snail has been negligently overlooked in the list for Delaware or New Jersey. Planorbella campanulata, Physella gyrina, P.
acuta, P. heterostropha – who gives a S**T.
It’s f***ing Delaware and New
Jersey and it’s not the FOCUS OF THE PAPER – which if you need reminding is
about conservation of rare species.”

A species can be rare only by comparison with other species. Unless we know what is common, we cannot
recognize what is rare. The comment
above reminds me of the frat brother who said he’d rather have two slices of pizza than half a pizza, because he “didn't give a S**T about denominators.”

Notes

[1] The 2013 data and analysis are available for download here - [PDF]

Despite being entitled “Natural Heritage Program List of
Rare Plant Species of North Carolina 2012” and “Natural Heritage Program List
of Rare Animal Species of North Carolina 2012,” neither of these reports has much
to do with rarity. Both seem to be
focused almost entirely upon such unscientific categories as “endangered,”
“threatened,” “imperiled,” “vulnerable,” and “secure.” A definition for “significantly rare” is,
however, to be found at the bottom of page 6 in the plants list.

[6] None of Gaston’s
20 examples included any references to the voluminous gray literature generated
by natural heritage agencies here in the USA - state, federal, or NGO. I cannot pretend to more than passing
familiarity with any of it, myself. But
in the few cases of which I am aware, such as the NC “Rare Plants List” cited
above, rarity definitions are incomplete.
Gaston might have summed up the “significantly rare” species of plants
in North Carolina for his numerator, but we are not given the total species
count for our denominator.

[7] Plagiarism, Paul Johnson, and The American Fisheries
Society. [9Sept13]